Wave breaking is observed in a laboratory experiment with waves of realistic average steepness and directional spread. It is shown that modulational-instability mechanism is active in such circumstances, and can lead to the breaking. Experiments were conducted in the directional wave tank of the University of Tokyo, and the mechanically-generated wave fields consisted of a primary wave with sidebands in the frequency domain, with continuous directional distribution in the angular domain. Initial steepness of the primary wave and sidebands, as well as the width of directional distributions varied in a broad range, in order to determine the combination of steepness/directional-spread properties which separate modulational-instability breaking from the linear-focusing breaking.